Solve for $x$ and $y$ using elimination. ${-2x+3y = 12}$ ${2x-5y = -24}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $-2y = -12$ $\dfrac{-2y}{{-2}} = \dfrac{-12}{{-2}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-2x+3y = 12}\thinspace$ to find $x$ ${-2x + 3}{(6)}{= 12}$ $-2x+18 = 12$ $-2x+18{-18} = 12{-18}$ $-2x = -6$ $\dfrac{-2x}{{-2}} = \dfrac{-6}{{-2}}$ ${x = 3}$ You can also plug ${y = 6}$ into $\thinspace {2x-5y = -24}\thinspace$ and get the same answer for $x$ : ${2x - 5}{(6)}{= -24}$ ${x = 3}$